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Unformatted text preview: Econ 100
Fall 1998
Midterm 1
Section 001 PARTIAL CREDIT WILL ONLY BE GIVEN IF YOU SHOW ALL OF YOUR
WORK. 1. Jane consumes only two goods: popcorn and soda. Bundle W includes 5 bags of
popcorn and 2 sodas. Bundle F includes 3 bags of popcorn and 6 sodas. Bundle V
includes 4 bags of popcorn and 1 soda. Jane prefers bundle F to bundle’W. ‘ a) Which bundle will she prefer? Bundle W or bundle V? Which axiom do you use.
to answer this question? (6 points) ' (3,0) 7(53) ‘> (9,1) W>V by noriStLHaih'on
F‘ N V ' . a ' A ' b) Which bundle will she prefer? Bundle F or bundle V? Which axiom do you use
to answer this question? (6 points) F>\/ b3 tmnsiﬁw'ij Justin likes doing two things: watching TV shows and playing hockey. He doesn’t
spend any time doing anything else. Yesterday, Justin spent 10 hours watching TV
and 14 hours playing hockey. His utility function is U=(T,H)=.T2 + H where T
denotes the number of hours spent watching TV and H denotes the number of hours
spent playing hockey. a) What is a feasible combination of TV and hockey that will make Justin even
happier than he is when he watches 10 hours of TV and plays 14 hours of hockey? (4points) UUOJd) = goo-Hi1 ML} ﬁnd ‘T1H Sudn‘tiﬁat
U(1jH):>HLl but T+H’=7_'-( T=n H=l3 —9 ohms): Ill + :3 =15‘i il b) What is Justin’s budget constraint? (4 points) 'T-t-szul c) Calculate Justin’s MRS when he consumes 10 hours of TV and 14 hours of
hockey. (4 points) 3’5. (WIN
3U/aH a
:"TT—4ZO . Jeremy’s preferences for good X and good Y can be summarized with the following. utility function: U(x,y)=(2X+2)(Y+l). Jeremy has $161 to spend on X and Y. X
costs $1 per unit and Y costs $2 per unit. a) Write down an expression describing J eremy’s marginal rate of substitution
between X and Y. (5 points) U: ax~f+aY +ax+ .1 mKS= ’aU/ax g "(w/+9) = ,EL'
39/23 (am-3) X+l b) When Jeremy has 9 units of X and l9'units of Y, how many units of X is he
willing to trade in for another unit of Y? (5 points) mas: ‘22.- ..
no" 2 60 M is uill1h5 +0 84% via "a unit of
_><' 1Q)!“ GnonEr 3. c) Given Jeremy’s constraints, how much X and Y will he choose to consume? (10
points) m as ~= “1;”; Y4»! L __ l 9 'ZJ‘ft-Z z X‘l'l
X+| " 2*?“ a x up: = X+ lY =: ZYH +2.1’ Y ﬁler; X 4. Bob’s demand curve for milkshakes is X =-- —3f;3 + Py + 2 , where X is the number of
milkshakes he consumes and Y is another good. a) Is Y a substitute for milkshakes. or a complement? Why? ( 3 points)
HSSmeS ‘1’ ﬂat (53W , PD T =) thﬂ. Hum 66} Utrth that 1‘93 4 TX 60 13 g‘ Lx means Jubseﬁhl'ieS. b) Use calculus to write an equation that describes the price elasticity of demand for
good X. (5 points)
eaRB ﬁx'Ei: X “Cl-PXQ' ~
x c) When milkshakes cost $1 a piece and Bob consumes 4 of them, what is his price elasticity of demand for milkshakes? Is his demand for x elastic, inelastic or unit
elastic? (5 points) “19.3 = ‘3.
LI ‘1! 9105+? c. (1) Based on your answer to c) what will happen to the revenues of a milkshake
stand if it raises the price of milkshakes from $1 to $2? Why? (5 points) [ZAQ‘> mam smacksqu
so {WU-Ea will pa“.
(:3ch Qua/mm.) of millcshalcﬂo Qlls alot) 5. a) Are the two goods on the diagram below complements or substitutes? Why? (5
points) 19:11.: Page: Oomr’l *1me ~ when WWBW Hut Prick of Pi 1241
‘Collsﬂrlxe (ﬁrms ‘lﬁ‘Uh
0F bO‘Hﬁ (3)00 ’ r {52.3. (“Quits b) Based on your answer to a), what will happen to the demand curve for pizzas
when the price of movies falls? Show below. (3 points) P? {not P I. 2:2 a
c) On the diagram in part a) draw the price consumption curve and label it. (3 points) . Use the diagram below to answer the following questions.
a) Are X and Y complements or substitutes? (3 points) b) Is Y a normal good or an inferior good? (3 points)
0) Is Y a Giffen good? (5 points) 7. Use the diagram below to answer the following questions. Note that px=1. a) How much income does this consumer have? (4 points) is 5 0
Circle all of the following words that describe the relationship between the two
goods: (4 points—you lose 2 points for each wrong choice here) substitutes,erfect complement unit elastic, perfect substitutes, no relationship. b) If the consumer chooses bundle A, what is the price of Y? (4 points)
if 2 d) If the consumer chooses bundle A, how much Y does he consume? (4 points) 16’ If the consumer chooses bundle B, how much X and how much Y does he
choose? (10 points) 1:350 ...
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